My professor wants an example of the Schroeder-Bernstein Theorem (If the card A<card B and card B<card A, then card A = card B).

He wants us to use , and to be and to be .

There is a proof sketch in the book, and he wants us to work through that using our example functions and sets. I'm just confused about the notation here:

Define and and . Then for each define:

How do I put into this? I want to say that they're all just but I'm not sure. Help!

Thank you!!